Question 129

In a survey of 300 students of a junior school, it was found that 45% students liked art class, 51% liked sports class, and 64% liked music class. Also, 29% liked art and sports classes both, 25% liked music and sports classes both, and 32% liked art and music classes both. 6% did not like any of the three classes.
What is the number of students who like only one of the three classes?

Untitled

s + 2d + 3t = 45 + 51 + 64 = 160 where "s" represents number of students who like only one of the three classes, "d" represents number of students who like only two of the three classes and "t" represents number of students who like all of the three classes.
s + d + t = 100 - 6 = 94.
By subtracting these equations, we get: d + 2t = 66. 
d = 29-X + 32-X + 25-X = 86 - 3X and t = X.
86-3X + 2X = 66 ==> X = 20.
t = 20 and d = 26. This gives s = 94 - 26 - 20 = 48.
So, the students who like only one of the three classes are 48% of the Total number of students i.e. 48% of 300 = 144.

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